According to VNDB (for both Aoishiro and Akai Ito) and the Manga Updates page for Aoishiro - Kaeishou, Akai Ito is the sister game to Aoishiro.
From what I can tell, they are both Shoujo Ai/Yuri titles, both done by Success and both seem to focus on Oni. However I can't see how those elements would make Aoishiro and Akai Ito sister games.
So I am wondering, is there some sort of connection between the 2?
I imagine the most significant of your mentioned connections is that they are created by the same developer - Success.
Having similar themes and a similar art style is definitely enough to warrant the title of sister games.
As a Western example, Bastion and Transistor are also sister games - They share no common story, but are similar in artistic style, development company, musician and artist.
The term sister in sister-game is broad and stems from sister cities & sister companies. The latter of which shares no more than the same parent company. Sister cities are broad, officially approved, long-term partnerships between two communities - but they do not have to be culturally alike or share many traits.
The requirements for shows to have an implicit connection is low, and can be justified by being in the same broad universe, parallel universe, etc. It's mainly a production choice.
